Problem: Simplify the following expression: $k = \dfrac{-24r + 60}{-24r - 12}$ You can assume $r \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-24r + 60 = - (2\cdot2\cdot2\cdot3 \cdot r) + (2\cdot2\cdot3\cdot5)$ The denominator can be factored: $-24r - 12 = - (2\cdot2\cdot2\cdot3 \cdot r) - (2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $k = \dfrac{(12)(-2r + 5)}{(12)(-2r - 1)}$ Dividing both the numerator and denominator by $12$ gives: $k = \dfrac{-2r + 5}{-2r - 1}$